There's a 95% chance the problem is one of the parts I mentioned before. Which one do you want to guess at first, and try? Then which will you change next, and then next, knowing that all of them are old and highly suspect?
The cost for all of it is likely $300 or so for the parts, plus the one time labor. Why do part of it and pay similar labor for each part, or a guess of a part or parts, and then have to do the rest soon enough later on? To me that's being a cheapass, a rebuild will be $2500+, but you balk at $300 and try to save $200 by skipping many of those important parts. Do it right, do them all, one time, in one step. Then if it doesn't work great, then you can expect it to require a rebuild. If you don't do it all, and something still isn't right, you are back where you were, and guessing again.